Rewrite as a simplified fraction. ${0.21\overline{3} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 213.3333...\\ 100x &= 21.3333...\end{align*}}$ Subtracting the two equations, we have: ${900x = 192}$ ${x = \dfrac{192}{900}} $ ${x = \dfrac{16}{75}} $